Graph theory has put forward a mathematical foundation for modelling and fine tuning communication and transportation networks. Centers and path centers serve as effective tools for optimizing traffic flow and efficiently allocating resources. The present article examines the concepts of eccentricity, center and path center of a fuzzy graph based on & micro;-distance. The major contribution of this article is an algorithm to find the path center and center of trees in fuzzy context. Many characteristics of center and path center of fuzzy graphs are explored and illustrated. Furthermore, eccentricities of adjacent nodes in a fuzzy graph and eccentricities of end nodes of effective arcs and strongly & micro;-related nodes are investigated.
The work is devoted to the control of the technological process of obtaining polypropylene by alkalizing, washing and drying the propane propylene fraction (PPF). As a scientific innovation in the presented work, the following should be noted: 1) For the first time, a dynamic expert system has been created for the technological process of obtaining polypropylene by the above-mentioned method; 2) A dynamic database has been developed that provides storage and use of fractographic data used in the management of the technological process of obtaining polypropylene; 3) Appropriate instrumentation have been selected and their activities in the system have been provided for the full automatic implementation of the processes of production, primary processing and maintenance of the regime parameters of the technological process; 4) Algorithms for the initial processing of setting values of parameters for the management of the technological process have been developed; a complex of relevant programs for questioning and processing of transmitters has been created. To ensure the security of the database developed by me in SQL Server, it is first necessary to create users and assign them appropriate access privileges, including management, data editing, device addition, and other related operation.
The main purpose of this article is to introduce the notion of d(v)-point in a vector metric space which is a generalization of the notion of d-point in metric spaces and extend Weston's characterization of metric completeness to vector metric spaces in terms of d(v)-point. In fact, we have utilized the concepts of lower semicontinuity and uniform continuity in this new framework to establish the main result. Finally, we established relations among minimal points, d(v)-points and fixed points in this new setting. As an application of this study, we obtained the analogue of Banach Contraction Principle in vector metric spaces.
Explained variation measures are very popular in regression models. They explain the amount of variation in the dependent variable by the explanatory variables. In some situations, a small sample size is available in comparison to the number of explanatory variables. In this case, explained variation measures may become significantly inflated. In order to tackle this problem, adjusted explained variation measures are used. In this work, we propose adjusted explained variation measures depend on the deviance for zero-inflated Poisson regression model (ZIPRM). We compare the performance of the suggested measures with that of the unadjusted explained variation measures for the ZIPRM using a Monte Carlo simulation experiment and real datasets.
In this paper, we introduce the concept of fuzzy general disjointness property along with its notation. Our results indicate that a fuzzy section semi-complemented lattice possesses the fuzzy atomic covering property if it meets the criteria for the fuzzy atomic disjointness property. Furthermore, we establish that if a fuzzy section semicomplemented lattice satisfies the fuzzy disjointness property, then it is both fuzzy 1modular and a fuzzy Birkhoff lattice.
Fuzzy set theory has been proven to be a powerful tool for dealing with uncertainty in decision-making processes. This theory addresses uncertain parameters. Soft set theory is another mathematical concept used for managing uncertainty in decisionmaking processes and imprecision. Integrating the ideas of a fuzzy set and a soft set, Jun et al. established the concept of hybrid structure. We should emphasize that hybrid structures combine soft and fuzzy set theories. The main objective of this paper is to explore the concept of hybrid bi-ideals and hybrid quasi-ideals in ordered semirings. In addition, we construct an example of hybrid bi-ideal and hybrid quasi-ideal in an ordered semiring. We provide various properties of hybrid bi-ideal and hybrid quasi-ideal in ordered semirings.
This mathematical model consists of three nonlinear ordinary differential equations between two prey (N-1, N-2) and only one predator (P). The two prey (N-1, N-2) grow logistically under predator pressure, and the predator depends mainly on the first prey (N-1). According to function response Holling's type II formula, indirect competition exists between N1 and N-2 because the predator exerts strong pressure on first prey (N-1), while second prey (N-2) is affected more simply. Equilibrium points for the mathematical model between predator and two prey, which stabilize over time, were calculated, and the local stability around the equilibrium points of this proposed model was analyzed using the Lyapunov function. Finally, numerical simulation was used to demonstrate the results.
This article introduces a distinct collection of fixed point iteration schemes. For this collection, a strong convergence result is established involving weak contractions. Additionally, a comparison result is obtained to compare the speed of convergence of different iterations in the collection. Furthermore, a result comparing some iterations from the collection with several notable and recent iterative schemes from the literature is procured. Finally, these comparisons are elucidated by a non-trivial exemplification, which is represented graphically as well. This family of iterations is conjectured to be the fastest in literature for steps more than three.
This work is focused on the construction of numerical schemes with higherorder accuracy in space and time to solve the time-fractional Black-Scholes model that governs the price of European options. We develop three numerical schemes utilizing the fourth-order Pade approximation, a fourth-order Taylor's compact difference scheme and a fourth-order compact exponential scheme for spatial discretization. We employ L1-2-3 approximation of order 4 - alpha, 0 < alpha < 1, to discretize the time-fractional derivative. In addition, the solvability, convergence, and stability of these numerical schemes are established. Numerical experiments are conducted to demonstrate the accuracy of the proposed schemes and validate the theoretical findings. The new proposed schemes offer higher and better accuracy.
Recently, exponent matrices have emerged as a dynamic tool for studying networks by measuring node centrality. In this work, we define a Symmetric Neighbors degree sum exponent matrix SNE(G) of a graph G whose (i, j)(th) entry is delta(delta j)(i) + delta(delta i)(j) for i =/ j, it is zero otherwise, where delta i is the Neighbors degree sum of a vertex viin G. Inspired by the applications of Neighbors degree sum in redefining various degree based topological indices, we introduce characteristic polynomial of SNE(G), termed as Symmetric Neighbors degree sum exponent polynomial and the sum of absolute value of eigenvalue of SNE(G) matrix is called as Symmetric Neighbors degree sum exponent energy. In this paper, we obtain the Neighbors degree sum exponent polynomial and Neighbors degree sum exponent energy of some graphs.
The purpose of this paper is to define and study a new class of sets called Pythagorean fuzzy nano delta (resp. delta pre, delta semi, delta alpha and delta beta)-open sets in Pythagorean fuzzy nano topological spaces. Analyse the basic properties of Pythagorean fuzzy nano delta (resp. delta pre, delta semi, delta alpha and delta beta)-open (resp. closed) sets. We also used them to introduce the new notions like Pythagorean fuzzy nano delta (resp. delta pre, delta semi, delta alpha and delta beta)-closure (resp. interior) and investigate their relations with already existing well known sets. We apply entropy measure for decision making problem of selecting the optimum wastewater treatment method for the dying factories based on the required criteria.
This paper studies strongly *-graphs as a variation of strongly multiplicative graphs. We show that every strongly multiplicative graph induces a strongly *-graph. We establish a relationship between the upper bounds on the number of edges of strongly *-graphs lambda*(n) and strongly multiplicative graphs, and identify a condition under which the upper bound for strongly *-graphs exceeds that of strongly multiplicative graphs, we show that this condition holds for infinitely many values of n. We derive explicit formulas for lambda*(n). Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly*-labeling.
In this paper we define fuzzy weak essential submodules to introduce the concept of fuzzy W-closed submodules of an R-module M. Further, we define fuzzy fully semiprime module. We use the condition of fuzzy fully semiprime module to show that a non-constant fuzzy closed submodule is W-closed in M. Also, the chain condition on fuzzy W-closed submodules is studied.
. In this paper, we establish few fixed point results in multiplicative metric space and prove the existence of fixed points along with its uniqueness, by employing contraction mappings in complete multiplicative metric space. We have provided few examples to validate our obtained results. Furthermore, we prove some theorems involving solutions of nonlinear integral equation as an application of our fixed point theorems.
By using Interpolative Hardy-Rogers type contraction via w-admissibility approach in the framework of quasi-partial metric space, we introduce a new property that makes it convenient to investigate the existence and uniqueness of fixed point theorems.
The eccentricity matrix of a graph G is derived from its distance matrix by letting the ij(th) entry be equal to the distance between two vertices i and j, if the distance is the minimum of their eccentricities and zero otherwise. The eigenvalues of the eccentricity matrix of G are called epsilon-eigenvalues. Its epsilon-spectrum is the set of epsilon eigenvalues together with its multiplicity and epsilon-energy is the sum of the absolute values of the epsilon-eigenvalues. In this paper, we study the epsilon-spectra of certain operations on regular graphs. We also established some bounds on epsilon-energy of graphs and characterize the extreme graphs.
A fresh scrutinize at boosting complex network dependability comes through applying the Sea Lion Optimization technique. Three distinct cost functions shape wherein these networks are built, each targeting unique design factors. Reaching higher reliability without pushing expenses too high stands as the main aim present This balance grows stronger because SLO steers clear of dead-end solutions while moving steadily toward better results. Tests show noticeable gains in by what means evenly reliability spreads across systems when contrasted with older strategies. Flexibility allows integration into multiple real-world setups where performance matters. The results confirm that the SLO-based approach is effective along with applicable for solving network reliability improvement problems.
In this work, we consider problems of S-4 and p-convex partition separations with respect to the all-path and the detour convexities. We give characterizations of p-all-path convex and p-detour convex graphs. With respect to all-path convexity S-2, S-3, and S-4 separable graphs are characterized. Also, we present necessary and sufficient conditions for two sets to be S-4 separable, for both convexities. Moreover, we prove that in all-path convexity the time complexity of those problems is linear, and it is NP-hard for detour convexity. Finally, we give an algorithm for determining whether two sets in graph are S4 separable with respect to all-path convexity.
The aim of this article is to estimate the magnitude of asset price jump sizes using an inverse method applied to historical financial data. Specifically, we adapt a particular form of the Merton jump-diffusion model for this estimation. The model is then discretized using the characteristics of the Poisson process along with the Euler-Maruyama numerical method. Using historical financial data from various assets including global gold ounce prices, Alphabet (Go ogle) stock, and crude oil collected over 2, 6, and 5-year periods, we estimate the price jump size for a short one-week time frame for these assets. This estimation is carried out by minimizing the price jump size inversely, using the discretized function obtained from the Euler-Maruyama numerical method, implemented through simulation in Python software. Finally, the effectiveness of the inverse method in estimating asset price jump sizes is evaluated by comparing the estimated values with the actual observed price jump sizes in the historical data of each asset, taking into account the calculated error.
In this paper, we study the existence of periodic solutions for a kind of first-order impulsive differential equation with a deviating argument by using Mawhin's continuation theorem. Meanwhile, we give an exampleto demonstrate our result.
